Abstract: Two types of higher order Lie l-ple systems are introduced in this paper. They are defined by brackets with l > 3 arguments satisfying certain conditions, and generalize the well-known Lie triple systems. One of the generalizations uses a construction that allows us to associate a (2n – 3)-Leibniz algebra pound with a metric n-Leibniz algebra () pound over tilde by using a 2(n – 1)-linear Kasymov trace form for () pound over tilde. Some specific types of k-Leibniz algebras, relevant in the construction, are introduced as well. Both higher order Lie l-ple generalizations reduce to the standard Lie triple systems for l = 3.

Abstract: We solve the modified non-linear extension of the CCFM equation – KGBJS equation – numerically for certain initial conditions and compare the resulting dipole amplitudes with those obtained front solving the original CCFM equation and the BFKL and BK equations for the same initial conditions. We improve the low transversal momentum behaviour of the KGBJS equation by a small modification.

Abstract: We prove that the present experimental constraints are already enough to rule out the possibility of the similar to 125 GeV Higgs found at LHC being the second lightest Higgs in a general MSSM context, even with explicit CP violation in the Higgs potential. Contrary to previous studies, we are able to eliminate this possibility analytically, using simple expressions for a relatively small number of observables. We show that the present LHC constraints on the diphoton signal strength, tau tau production through Higgs and BR(B -> X-s gamma) are enough to preclude the possibility of H-2 being the observed Higgs with m(H) similar or equal to 125 GeV within an MSSM context, without leaving room for finely tuned cancellations. As a by-product, we also comment on the difficulties of an MSSM interpretation of the excess in the gamma gamma production cross section recently found at CMS that could correspond to a second Higgs resonance at m(H) similar or equal to 136 GeV.

Abstract: We have investigated the structure and energetics of mixed He-3-He-4 droplets doped with a carbonyl sulfide molecule within a density functional approach considering a small but finite temperature of 0.1 K. The molecule is treated as an external field to which the helium droplet is attached. The energetics and appearance of these droplets are discussed for selected numbers of helium atoms, identifying the first magic numbers of the fermionic component.

Abstract: We analyze oriented event-shapes in the context of Soft-Collinear Effective Theory (SCET) and in fixed-order perturbation theory. Oriented event-shapes are distributions of event-shape variables which are differential on the angle theta(T) that the thrust axis forms with the electron-positron beam. We show that at any order in perturbation theory and for any event shape, only two angular structures can appear: F-0 = 3/8 (1+cos(2) theta(T)) and F-1 = (1 – 3 cos(2) theta(T)). When integrating over theta(T) to recover the more familiar event-shape distributions, only F-0 survives. The validity of our proof goes beyond perturbation theory, and hence only these two structures are present at the hadron level. The proof also carries over massive particles. Using SCET techniques we show that singular terms can only arise in the F-0 term. Since only the hard function is sensitive to the orientation of the thrust axis, this statement applies also for recoil-sensitive variables such as Jet Broadening. We show how to carry out resummation of the singular terms at (NLL)-L-3 for Thrust, Heavy-Jet Mass, the sum of the Hemisphere Masses and C-parameter by using existing computations in SCET. We also compute the fixed-order distributions for these event-shapes at O(alpha(S)) analytically and at O(alpha(2)(S)) with the program Event2.